On stable region-of-interest reconstruction in tomography: examples of non-existence of bounded inverse. (8th November 2016) - Boman, Jan
Abstract: In applications of computerized tomography (CT) it is often of interest to reconstruct a function in a proper subset, the region of interest (ROI), of its support from a proper subset of a full CT-scan. In several recent works it has been shown that stable ROI reconstruction is possible in certain limited data situations. In this paper we investigate the limits of what is possible in that direction by proving that reconstruction in an interior ROI is severely unstable for a certain set of data that contains integrals over all lines that intersect the ROI and is large enough for the unknown function to be uniquely determined.